WASHINGTON — President Obama personally apologized on Wednesday to the head of Doctors Without Borders for what he described as the mistaken bombing of its field hospital in Kunduz, Afghanistan, promising a full investigation into the episode, which took the lives of nearly two dozen doctors and patients.

But five days after an American AC-130 gunship devastated the medical facility, Mr. Obama’s personal expression of regret in a telephone call from the Oval Office appeared to do little to satisfy the leader of the doctors group, who issued a terse statement saying the president’s apology had been “received.”

Dr. Joanne Liu, the international president of Doctors Without Borders, repeated her demand for an independent investigation led by the International Humanitarian Fact-Finding Commission to “establish what happened in Kunduz, how it happened, and why it happened.”

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Dr. Joanne Liu, the president of Doctors Without Borders, spoke on Wednesday in Geneva.Credit
Denis Balibouse/Reuters

White House officials said the president had confidence that the investigative effort now underway, including an inquiry being conducted by the Department of Defense, would be “transparent, it will be thorough, and it will be objective.”

Direct presidential apologies to victims of American actions abroad are rare, but not unheard-of. In 2012, Mr. Obama wrote a letter of apology to President Hamid Karzai of Afghanistan after several copies of the Quran were burned by American military personnel, leading to violent protests across that country. In 2004, President George W. Bush apologized for the treatment of Iraqi prisoners at the Abu Ghraib military prison, telling world leaders that he was “sorry for the humiliation.”

Whether to deliver an apology is a difficult and sensitive decision for any president, but particularly for this one. Mr. Obama has been pilloried since the beginning of his presidency by Republicans who accuse him of being a serial apologizer for America. Mitt Romney, the Republican candidate for president in 2012, wrote a book titled “No Apology,” a not-so-subtle dig at Mr. Obama. And Dick Cheney, the former vice president, recently published a book renewing the apology criticism of the president.

In this case, Mr. Obama proceeded with caution. Two days after the bombing, he expressed his “deepest condolences” to families of the hospital victims, calling it a “tragic incident.” But he and other White House officials resisted further comment for several days, citing the need to let investigations continue.

That changed on Wednesday after grim and detailed congressional testimony by Gen. John F. Campbell, the American commander in Afghanistan, who told lawmakers the attack was “a U.S. decision made within the U.S. chain of command.”

At the White House on Wednesday, Josh Earnest, the press secretary, said that “when the United States makes a mistake, we own up to it, we apologize.” He explained the shift in the decision to apologize by saying that Mr. Obama had decided “that he had learned enough about this matter to conclude that it was appropriate for him to offer an apology.”

White House officials said Mr. Obama told Dr. Liu that he would make any changes necessary to ensure that such incidents were less likely in the future. And they said that the president promised a “full accounting” of who was to blame, and whether the military’s rules of engagement need to change.

That may not be enough for Doctors Without Borders, which has said they do not believe the three investigations that have been begun into the incident — by NATO and a joint United States-Afghan group and the Defense Department — are independent enough to find the truth about what happened.

In her statement responding to Mr. Obama’s call, Dr. Liu reiterated the organization’s request that the United States “consent to an independent investigation led by the International Humanitarian Fact-Finding Commission.”

The use of the word “consent” in her statement was central to the group’s demand that the United States endorse a more independent investigation. The International Humanitarian Fact-Finding Commission, a body set up under the Geneva Conventions, can investigate violations of international humanitarian law, but only if the countries involved give their permission. In this case that would mean extracting the blessings of both Afghanistan and the United States, which seems unlikely.

The commission is made up of 15 members, elected by the 76 countries that recognize its authority. Neither the United States nor Afghanistan is among the 76. The commission was created in 1991 but has never been used.

At a news conference in Geneva on Wednesday, Dr. Liu said that patients at the Kunduz hospital burned in their beds, and that doctors, nurses and other staff members were killed as they worked. “Our colleagues had to operate on each other,” she said. “One of our doctors died on an improvised operating table — an office desk — while his colleagues tried to save his life.”

What Is the International Humanitarian Fact-Finding Commission?

Jason Cone, the executive director of Doctors Without Borders in the United States, said that the organization’s staff called the office of the chairman of the Joint Chiefs of Staff during the bombardment of the hospital. Mr. Cone would not discuss the contents of the calls, saying that Doctors Without Borders wanted to preserve the privileged nature of its communications with the government.

But he did say that the chairman’s office was the same office to which Doctors Without Borders had provided GPS coordinates for the hospital on Sept. 30. The group also provided the same GPS coordinates to the American-led coalition in Afghanistan on Sept. 29.

Mr. Cone could not say who or what office at the American-led coalition in Afghanistan was contacted during the attack.

“All we know is that our one hospital was struck repeatedly after we told them where we were located, and called them in desperation to stop the attack,” he said.

The targeting of a medical facility is considered a war crime, if it is proved to be deliberate. But attacks on medical facilities have occurred with some regularity, and assessing whether they were deliberate has been difficult. On Wednesday, Physicians for Human Rights, an advocacy group, said it had confirmed that Russian airstrikes had damaged three medical facilities in Syria.

“With these actions, Russia is damaging hospitals, putting patients and medical staff at risk, and depriving civilians of lifesaving access to health care,” the group said in a statement.

Michael D. Shear reported from Washington, and Somini Sengupta from the United Nations. Matthew Rosenberg contributed reporting from Washington, and Nick Cumming-Bruce from Geneva.